100=(1/2)*(z*0.8660254038)

Solution for 100=(1/2)*(z*0.8660254038) equation:

100=(1/2)(z*0.8660254038)

We move all terms to the left:

100-((1/2)(z*0.8660254038))=0


Domain of the equation: 2)(z*0.8660254038))!=0

z∈R


We add all the numbers together, and all the variables

-((+1/2)(+z*0.8660254038))+100=0

We multiply parentheses ..

-((+0.8660254038z^2))+100=0


We calculate terms in parentheses: -((+0.8660254038z^2)), so:

(+0.8660254038z^2)

We get rid of parentheses

0.8660254038z^2

Back to the equation:

-(0.8660254038z^2)


We get rid of parentheses

-0.8660254038z^2+100=0

a = -0.8660254038; b = 0; c = +100;
Δ = b2-4ac
Δ = 02-4·(-0.8660254038)·100
Δ = 346.41016152
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-\sqrt{346.41016152}}{2*-0.8660254038}=\frac{0-\sqrt{346.41016152}}{-1.7320508076}
=-\frac{\sqrt{}}{-1.7320508076}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{346.41016152}}{2*-0.8660254038}=\frac{0+\sqrt{346.41016152}}{-1.7320508076}
=\frac{\sqrt{}}{-1.7320508076}
$